integral of (x-3)(x-1)

Lösung

\int (x - 3) (x - 1) d x

\frac{x ^{3}}{3} - 2 x^{2} + 3 x + C

Schritte zur Lösung

\int (x - 3) (x - 1) d x

Multipliziere aus

(x - 3) (x - 1) : x^{2} - 4 x + 3

= \int x^{2} - 4 x + 3 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x - \int 4 x d x + \int 3 d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int 4 x d x = 2 x^{2}

\int 3 d x = 3 x

= \frac{x ^{3}}{3} - 2 x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 2 x^{2} + 3 x + C

\int \frac{4 x - 5}{( x - 1 ) ( x ^{2} + 1 )} d x

\int x (x - 10)^{10} d x

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\int \frac{- sec ^{2} ( x )}{5} d x